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Asset pricing at the millennium
 Journal of Finance
"... This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior ..."
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Cited by 123 (3 self)
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This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the tradeoff between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and crosssectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar* Department of Economics, Harvard University, Cambridge, Massachusetts
Dynamic consumption and portfolio choice with stochastic volatility in incomplete markets
, 2003
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A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability
, 2005
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Portfolio choice problems
 Handbook of Financial Econometrics, forthcoming
, 2004
"... After years of relative neglect in academic circles, portfolio choice problems are again at the forefront of financial research. The economic theory underlying an investor’s optimal ..."
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Cited by 24 (2 self)
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After years of relative neglect in academic circles, portfolio choice problems are again at the forefront of financial research. The economic theory underlying an investor’s optimal
Optimal versus Naive Diversification: How . . .
, 2007
"... We evaluate the outofsample performance of the samplebased meanvariance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Shar ..."
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Cited by 22 (1 self)
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We evaluate the outofsample performance of the samplebased meanvariance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certaintyequivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the samplebased meanvariance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many “miles to go” before the gains promised by optimal portfolio choice can actually be realized out of sample.
Dynamic Portfolio Selection by Augmenting the Asset Space
 THE JOURNAL OF FINANCE • VOL. LXI, NO. 5 • OCTOBER 2006
, 2006
"... We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in ..."
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Cited by 21 (3 self)
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We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in each asset an amount proportional to conditioning variables, and “timing” portfolios, which invest in each asset for a single period and in the riskfree asset for all other periods. The static choice of these managed portfolios represents a dynamic strategy that closely approximates the optimal dynamic strategy for horizons up to 5 years.
Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds
, 2007
"... The covariance between US Treasury bond returns and stock returns has moved considerably over time. While it was slightly positive on average in the period 1953— 2005, it was particularly high in the early 1980’s and negative in the early 2000’s. This paper specifies and estimates a model in which t ..."
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Cited by 20 (1 self)
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The covariance between US Treasury bond returns and stock returns has moved considerably over time. While it was slightly positive on average in the period 1953— 2005, it was particularly high in the early 1980’s and negative in the early 2000’s. This paper specifies and estimates a model in which the nominal term structure of interest rates is driven by five state variables: the real interest rate, risk aversion, temporary and permanent components of expected inflation, and the covariance between nominal variables and the real economy. The last of these state variables enables the model to fit the changing covariance of bond and stock returns. Log nominal bond yields and term premia are quadratic in these state variables, with term premia determined mainly by the product of risk aversion and the nominalreal covariance. The concavity of the yield curve–the level of intermediateterm bond yields, relative to the average of short and longterm bond yields–is a good proxy for the level of term premia. The nominalreal covariance has declined since the early 1980’s, driving down term premia.
The term structure of the riskreturn tradeoff
 Financial Analysts Journal
, 2005
"... Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. This paper has two objectives. First, we propose an empirical ..."
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Cited by 18 (1 self)
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Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. This paper has two objectives. First, we propose an empirical model that is able to capture the complex dynamics of expected returns and risk, yet is simple to apply in practice. Second, we explore the implications for asset allocation. Changes in investment opportunities have the important implication that the riskreturn tradeoff of bonds, stocks, and cash may be significantly different across investment horizons, thus creating a “term structure of the riskreturn tradeoff. ” We show how one can easily extract this term structure using our parsimonious model of return dynamics, and illustrate our approach using data from the U.S. stock and bond markets. We find that asset return predictability has important effects on the variance and correlation structure of returns on stocks, bonds and Tbills across investment horizons. Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. Starting at least
Predictable returns and asset allocation: Should a skeptical investor time the market
 Journal of Econometrics
, 2009
"... are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical inv ..."
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Cited by 16 (0 self)
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are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical investor time the market? We investigate optimal portfolio choice for an investor who is skeptical about the degree to which excess returns are predictable. Skepticism is modeled as an informative prior over the R 2 of the predictive regression. We find that the evidence is sufficient to convince even an investor with a highly skeptical prior to vary his portfolio on the basis of the dividendprice ratio and the yield spread. The resulting weights are less volatile and deliver superior outofsample performance as compared to the weights implied by an entirely modelbased Are excess returns predictable, and if so, what does this mean for investors? In classic studies of rational valuation (e.g. Samuelson (1965, 1973), Shiller (1981)), risk premia are constant over time and thus excess returns are unpredictable. 1
Does the failure of the expectations hypothesis matter for longterm investors?
, 2003
"... We consider the consumption and portfolio choice problem of a longrun investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond pr ..."
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Cited by 13 (4 self)
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We consider the consumption and portfolio choice problem of a longrun investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a threefactor Gaussian model with a timevarying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for timevarying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the longrun investor looks very different from the portfolio of a meanvariance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for longterm bonds.